On signed digraphs with all cycles negative (Q5903030)

The authors study the class \({\mathcal M}\) of the digraphs whose arcs can be signed (positive or negative) so that every directed cycle is negative. They identify certain family of such digraphs: upper digraphs and class \(\bar U,\) and characterize the symmetric digraphs of \({\mathcal M}\). Note that upper digraphs and class \(\bar U\) can be defined from a structure studied by the reviewer: the c-minimal strongly connected digraphs. That unifies and simplifies the proofs and answers to some authors's questions.